If itís a very small hole (3mm, quarter inch), a blob of kwik Grip, also known as contact adhesive, will do the job. Put a blob on the hole and on both sides of the screen and wait for it to be touch dry and then flatten the blob just a bit. This glue drys to be like rubber, not rock hard. Iíve done this four times, on two hammocks.
Mine were caused by the two zips. Now, before I pack the hammock away, I move both zips to one end of the hammock. I also put both pull out cords and shock cords inside the hammock, so that the cord locks are also at one end of the hammock. It was the zips, or cord locks that were causing the holes.